Nitride based semiconductor light-emitting device

1. A semiconductor device having a semiconductor multi-layer structure which includes at least an active layer having at least a quantum well, and said active layer further including at least a luminescent layer of In x Al y Ga 1-x-y N (0<x<1, 0≦y≦0.2),

wherein a threshold mode gain of each of said at least quantum well is not more than 12 cm −1 , and

wherein a differential gain “dg/dn” of said at least active layer satisfies 0.5×10 −20 (m 2 )≦dg/dn≦0.7×10 −20 (m 2 ).

2. The semiconductor device as claimed in claim 1 , wherein a standard deviation of a microscopic fluctuation in a band gap energy of said at least luminescent layer is in the range of 75 meV to 200 meV.

3. The semiconductor device as claimed in claim 1 , wherein said semiconductor device has an internal loss “α i ” (cm −1 ) which satisfies α i ≦12×n−α m (cm −1 ), where “α m ” is a mirror loss, and “n” is a number of said at least quantum well.

4. The semiconductor device as claimed in claim 1 , wherein said semiconductor device has a slope efficiency “S” (W/A) which satisfies:

S≧ 3×{α m /(12 ×n )}×[{(1 −R 1 )√{square root over ( )}(R 2 )}/{(1−√{square root over ( )}( R 1 R 2 ))×(√{square root over ( )}( R 1 )+√{square root over ( )}( R 2 ))}],

where “R 1 ” is a first reflectance of a first cavity facet, from which a light is emitted, “R 2 ” is a second reflectance of a second cavity facet opposite to said first cavity facet, “α m ” is a mirror loss, and “n” is a number of said at least quantum well.

5. The semiconductor device as claimed in claim 4 , wherein said semiconductor device has a cavity length “L” of not less than 200 micrometers, and each of said first and second reflectances “R 1 ” and “R 2 ” is not less than 80% and less than 100%, and said slope efficiency “S” satisfies S≧1.4/n (W/A).

6. The semiconductor device as claimed in claim 1 , wherein said semiconductor device has a photo-luminescence peak wavelength distribution of not more than 40 meV.

7. The semiconductor device as claimed in claim 1 , wherein said semiconductor multi-layer structure comprises a gallium-nitride-based multi-layer structure.

8. The semiconductor device as claimed in claim 7 , wherein said gallium-nitride-based multi-layer structure extends over a gallium-nitride-based substrate.

9. The semiconductor device as claimed in claim 7 , wherein said gallium-nitride-based multi-layer structure extends over a sapphire substrate.

10. The semiconductor device as claimed in claim 7 , wherein said gallium-nitride-based multi-layer structure extends over a substrate having a surface dislocation density of less than 1×10 8 /cm 2 .